Physics Practice Test 4

Which of the following is a dimensionally correct representation for angular momentum?

M2L2T-1

M2L1T-1

M2L1T-2

ML2T-1

ML1T-1

Correct Answer: D

Explanation:

Angular momentum is given as
L = Iω ------------ (1)
SI unit for I is kgm2. Hence, dimensional formula of I becomes ML2. Angular velocity is given as
ω = v/ r
SI unit of v is m/s and that of r is m. Hence, SI unit of angular velocity becomes
(m/s)/m Or 1/s
Therefore, dimensional formula of angular velocity is T-1 . Thus, dimensional formula of angular momentum from equation 1 becomes
ML2 / T Or ML2T-1
Hence, D is the correct answer option.

Question 2

A train at rest starts from station A and travels to station B at a distance of 2 km in 4 minutes? Consider the following statements.

Instantaneous speed of the train is 8.33 m/s

Average speed of the train is 8.33 m/s

Instantaneous acceleration of the train is 8.33 m/s2

Which of the following statement(s) is/are true?

1

2

3

Both 1 and 3

Both 2 and 3

Correct Answer: B

Explanation:

Instantaneous speed of a body is the speed possessed by it at any particular time instant. Instantaneous speed is a variable and changes accordingly. Speedometer is a device that is used by the vehicles to know the speed possessed by it at that instant. Average velocity or speed provides speed of the body for the full journey. It is given as the total distance travelled in total time taken. As in the question the total time and the total distance are given, hence average speed can be found as

Average speed = Total Distance / Total Time ------------- (1)

Since, distance and time are given in kilometers and minutes we need to convert them Putting the values in equation 1 we get

A water gallon of mass 500 kg is resting on a horizontal floor. What would be its normal reaction?

500 N

4900 N

5100 N

250 N

51.02 N

Correct Answer: B

Explanation:

As the water gallon is resting on the floor, normal reaction will be balanced by the weight of the gallon itself. Therefore,
Normal reaction = Weight of the gallon ------------- (1)
Weight of the gallon is given as
F = mg------------- (2)
Putting the values in equation 1 we get
F = 500 * 9.8 Or F = 4900 N
Using equation 1 we get
Normal reaction = 4900 N
Therefore, B is the correct answer option.

Question 4

A boy of 45 kg jumps out of a window and just before reaching the ground his speed is 2 m/s. After he hits the ground he stops and the total time taken during this process is 1 s. What is the force exerted by the ground on the boy?

45 N

22.5 N

180 N

90 N

85 N

Correct Answer: D

Explanation:

According toNewton’s second law of motion, force is time rate of change of momentum and is given as
F = p / t ------------ (1)
Momentum is given as
p = mv ------------- (2)
Putting the value of m and v in equation 2 we get
p = 45 * 2 Or p = 90 kgm/s
Putting the values of p and t in equation 1 we get
F = 90 N
Therefore, D is the correct answer option.

Question 5

A flying disc initially at rest rotates with a constant acceleration. If after 5 s the flying disc has rotated by 200 radians, what is its angular acceleration?

14 rad/s2

15 rad/s2

11 rad/s2

12 rad/s2

16 rad/s2

Correct Answer: E

Explanation:

Here we will apply theequation of rotational motion, which is given as

Two trains A and B approach a station at 10 m/s and 20 m/s respectively. A stationary observer in the station can hear the sound of the whistle produced by A only. If the original frequency of the whistle blown by train A is 300 Hz, what would be the apparent frequency of the sound of the whistle heard by the observer? (Assume speed of sound in air = 340 m/s)

300 Hz

291.42 Hz

283.33 Hz

318.75 Hz

309.09 Hz

Correct Answer: E

Explanation:

This question can be solved by applying Doppler’s effect for sound waves. Doppler’s effect is related to change in original frequency of sound if either the source or the observer is moving simultaneously. Doppler’s effect is given as
f = [(v - vr) / (v - vs]fo -------------- (1)
Putting the values in equation 1 we get
f = [(340) / (340-10]*300
f = (34/33)*300
Or f = 309.09 Hz
Therefore, E is the correct answer option.

Question 9

A body in a cubical shape of dimension and having mass of 2 kg is fully immersed in a fluid. What is the specific gravity of the body?

0.357

0.453

0.564

0.181

0.097

Correct Answer: A

Explanation:

Density is given as
ρ = m/V ------------- (1)

Volume of the body is given as
V = 0.7 * 0.1 * 0.08 Or V = 5.6 x 10-3m3
Putting the values in equation 1 we get
ρ = 2 / 5.6 x 10-3
Or ρ = 357.14 kg/m 3
Specific gravity is given as

A solenoid of length 60 cm and radius 2.4 cm carries current of 3 A. If the number of turns is 400, what is the magnetic field at the center of the solenoid on its axis? (Permeability of free space is 4π x 10-7 WbA-1m-1)

What would be the minimum angle of incidence so that a ray of light travelling from medium 1 of refractive index 1.7 to medium 2 of refractive index 1.5 does not emerge out of medium 2?

sin-1(0.88)

cos-1(0.88)

tan-1(0.88)

tan-1(1.13)

sin-1(1.13)

Correct Answer: A

Explanation:

For a ray of light incident on a medium to not emerge from it is known as limiting case of total internal reflection. For the minimum angle the refracted ray travels along the interface. For the incident ray making an angle more than the minimum angle the ray will reflect back and this is known as total internal reflection. From Snell’s law we have